CRYSTAL FIELD THEORY�

DEEPSHIKHA

DEPATRMENT OF CHEMISTRY

Crystal field theory (CFT) describes the breaking of orbital degeneracy in transition metal complexes due to the presence of ligands. CFT qualitatively describes the strength of the metal-ligand bonds. Based on the strength of the metal-ligand bonds, the energy of the system is altered. This may lead to a change in magnetic properties as well as color. This theory was developed by Hans Bethe and John Hasbrouck van Vleck.

Postulates Of Crystal Field Theory

The Postulates Of Crystal Field Theory are

1. In crystal field theory, we assume that the metal ion is surrounded by an electric field created by the ligands surrounding the metal ion.
2. The forces of attraction between the central metal ion and the ligand are considered purely electrostatic. The metal ion is targeted by the negative end of the dipole of the neutral molecule ligand.
3. The transition metal ion is a positive charge ion equal to the oxidation state.

4.The transition metal atom is surrounded by a specific number of ligands, which may be negative ions or neutral molecules having lone pairs of electrons.

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5.Ligands act as point charges that are responsible for generating an electric field. This electric field changes the energy of the orbitals on the metal atom or ions.

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6.The repulsive force between the central metal ion and ligand is responsible for the electrons of the metal ion occupying the d-orbitals as far as possible from the direction of approach of the ligand.

7.There is no interaction between metal orbital and ligand orbitals.

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8.In an isolated metal atom or ion, all the orbitals have the same energy, which means all the d-orbitals are degenerate. 

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9.If the central metal atom or ion is surrounded by the spherical symmetrical field of negative charges, the d-orbitals degenerate. However, the energy of orbitals is raised due to the repulsion between the field and the electron on the metal atom or ion.

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10. The d-orbitals are affected differently in most transition metal complexes, and their degeneration is lost due to the field produced by the unsymmetrical ligand.

Description of d-Orbitals

To understand CFT, one must understand the description of the lobes:

d_xy: lobes lie in-between the x and the y axes.

d_xz: lobes lie in-between the x and the z axes.

d_yz: lobes lie in-between the y and the z axes.

d_x²_-y²: lobes lie on the x and y axes.

d_z2: there are two lobes on the z axes and there is a donut shape ring that lies on the xy plane around the other two lobes.

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When examining a single transition metal ion, the five d-orbitals have the same energy (Figure 1) When ligands approach the metal ion, some experience more opposition from the d-orbital electrons than others based on the geometric structure of the molecule. Since ligands approach from different directions, not all d-orbitals interact directly. These interactions, however, create a splitting due to the electrostatic environment.

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For example, consider a molecule with octahedral geometry. Ligands approach the metal ion along the x, y, and z axes. Therefore, the electrons in the dz2 and dx2−y2 orbitals (which lie along these axes) experience greater repulsion. It requires more energy to have an electron in these orbitals than it would to put an electron in one of the other orbitals. This causes a splitting in the energy levels of the d-orbitals. This is known as crystal field splitting. For octahedral complexes, crystal field splitting is denoted by Δo(or Δoct). The energies of the dz2 and dx2−y2 orbitals increase due to greater interactions with the ligands. The dxy, dxz, and dyz orbitals decrease with respect to this normal energy level and become more stable.

Octahedral Complexes

In an octahedral complex, there are six ligands attached to the central transition metal. The d-orbital splits into two different levels . The bottom three energy levels are named dxy, dxz,and dyz(collectively referred to as t2g). The two upper energy levels are named dx2−y2,and dz2 (collectively referred to as eg).

The reason they split is because of the electrostatic interactions between the electrons of the ligand and the lobes of the d-orbital.

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In an octahedral, the electrons are attracted to the axes. Any orbital that has a lobe on the axes moves to a higher energy level. This means that in an octahedral, the energy levels of eg are higher (0.6∆_o) while t2g is lower (0.4∆_o).

The distance that the electrons have to move from t2g from eg and it dictates the energy that the complex will absorb from white light, which will determine the color.

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Whether the complex is paramagnetic or diamagnetic will be determined by the spin state. If there are unpaired electrons, the complex is paramagnetic; if all electrons are paired, the complex is diamagnetic

Crystal Field Splitting In Tetrahedral Complex

In a tetrahedral complex, there are four ligands attached to the central metal. The d orbitals also split into two different energy levels. The top three consist of the dxy, dxz, and dyz orbitals. The bottom two consist of the dx2−y2 and dz2 orbitals. The reason for this is due to poor orbital overlap between the metal and the ligand orbitals. The orbitals are directed on the axes, while the ligands are not.

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Tetraheral ligand field surrounding a central transition metal (blue sphere). 

The difference in the splitting energy is tetrahedral splitting constant (ΔtΔ, which less than (Δo) for the same ligands:

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Δt=0.44Δo

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Consequentially, ΔtΔ is typically smaller than the spin pairing energy, so tetrahedral complexes are usually high spin.

Square Planar Complexes

In a square planar, there are four ligands as well. However, the difference is that the electrons of the ligands are only attracted to the xy plane. Any orbital in the xy plane has a higher energy level There are four different energy levels for the square planar (from the highest energy level to the lowest energy level): d_x²_-y², d_xy, d_z², and both d_xz and d_yz.

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The splitting energy (from highest orbital to lowest orbital) is Δsp and tends to be larger then Δo

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Δsp=1.74Δo

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Moreover, Δsp is also larger than the pairing energy, so the square planar complexes are usually low spin complexes.

Limitations Of Crystal Field Theory

The limitations of crystal field theory are-

1. Crystal field theory could not account for the covalent bonding found in some transition metal complexes. 

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• It also fails to explain the order of ligands in the spectrochemical series. This is because ligands are considered point charges, and anionic ligands should have a stronger splitting effect. But anionic ligands are present at the bottom of the spectrochemical series. For example, the theory does not explain why water is a stronger ligand than hydroxide ions.

3.No contribution is considered for a and p orbitals, which is required in certain cases. This is a critical drawback because p-bonding is found in numerous compounds.

4.There is no discussion about the orbitals of the ligands in the transition metal. Thus the theory fails to explain properties related to ligand orbitals and their interaction with metal orbitals.

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